Glyphosate, along with citric acid as a water conditioner seem to clean my tanks out wonderfully. So I guess if that were me..... I would load the sprayer with water and citric acid (4#/100? )and agitate for awhile, then periodically spray the water out in the drive as the crud comes loose.

Or is the crud in the lines to the tips too? Leave the tips out.

Edit to add: would likely put a stiff dose of Dawn dish soap in too.